During the heyday of a bull market, it isn’t unusual to see the stock market generate annual returns of over twenty percent, or if you’ve aggressively invested in the Nasdaq of small company growth stocks, even thirty percent! These are the salad days when our financial goals are on track plus a little extra for that Porsche we’ve been admiring.

But all the celebrations must end. The economy is cyclical and at some point, the market will stutter, dropping 20% (a “correction”) or even as much as 50% (“Bear market”). What happened to all those awesome returns? Most have been wiped out, and we may spend the next several years getting back to where we were.

Yes, the market goes up more than it goes down. Over the long term we will make money, but how much exactly? As we’re trying to plan for our future, that’s an important number to know.

There are two ways to calculate the average return of the stock market. One is correct, the other not.

Calculating mean return

Let’s say you invest $100. Year one, you have a return of 100% (yay!), but in year two, you lose money, with a -50% return (boo!). What is your actual annual rate of return?

Did you calculate 25%?

Boo!

No, the real rate of return is 0%

In year 1, your $100 is now $200. But in year two, it loses 50% and is now $100 again. No gain.

The sequence doesn’t matter. Let’s say you lost 50% in year one but gained 100% in year two. $100 becomes $50, which then becomes $100 again. No gain.

When it comes to something as volatile as the stock market, using the arithmetic mean of returns is not correct. We all know the basic equation: add up all the items and divide by the number of items, or [100% + (-50%)] / 2 = 25%.

With the stock market our returns compound. If you have a return of 10% in year one followed by 10% in year two, that second gain applies to your original principal as well as all the gains made up to that point. $100 becomes $110, and then becomes $121 ($110 + 11).

For market drops, returns compound negatively, which acts to buffer some of the pain. For an annual 10% loss, $100 becomes $90, and then becomes $81 ($90-$9).

The correct method is to use the geometric mean, which accounts for compounding, both up and down. Note that the geometric mean will be less than the arithmetic mean.

When evaluating the rate of return in the real world, the correct number to use is the CAGR — compound annual growth rate.

The CAGR is like the geometric mean but is calculated a bit differently. Instead of calculating the mean of individual returns within a larger timeframe, the CAGR simply uses the starting balance, ending balance, and time to calculate a compounded rate.

CAGR in the real world

What exactly is the CAGR of the S&P500? As its name suggests, the S&P500 contains (approximately) 500 key stocks and is used as the key index of the market.

Depends on whom you ask, based on what timeframe is evaluated.

Below is a collection of CAGR calculations of the S&P500 TR, or “total return” including reinvested dividends. Most of the sources below rely on (free) historical data supplied by Robert Schiller.

DQYDJ provides a handy calculator for any timeframe desired; the last 20, 30, 40, and “all available” years are included below based on the calculator. Other estimates are from Stockmarketsanity, Krejca, and J.P. Morgan.

Interestingly, Stockmarketsanity, generates a projection for the next ten years.

TR = Total return = dividends reinvested. NR=not reported. *Calculated based on numbers provided

Results range from 6.6% annual total return to as high as 11% annual total return.

If all available S&P500 data is included, dating back to 1871, the CAGR is 9% or 6.8% after inflation. This number is quoted the most often.

However, estimates from the recent past (twenty years or less), along with the 10-year projection, are on the low end of the range at 6.6% That’s a lot less than the twenty-plus percent we get excited about.

Considering our current low interest-environment we forget that bonds used to make more than they do now. Indeed, there have been a few times in our history that bonds have outperformed stock. Which is another reason we should include bonds, along with stock, as part of a well-diversified portfolio.

Don’t forget about inflation

Inflation averages less than 3% at present but historically has been all over the place.

To correct for inflation, use the following formula:

After correcting for inflation, the real annual total return of the S&P500 ranges from a low of 4.3% to a high of 7.7%. Again, despite low inflation, the most recent past is on the low end at 4.3%.

Adjusting the 6.6% projected return with a 3% inflation rate results in only a 3.5% annual increase in purchasing power for the S&P500 moving forward.

Sigh.

For all those (sometimes sexy) returns you read about, ask the following questions: 1) is it a CAGR, 2) are reinvested dividends included, and 3) is inflation accounted for?

Likewise, what do you put at risk to get this sexy return? (The volatility, or risk, is measured by the standard deviation.) For you, is the risk worth it?

This will give you a more realistic idea of what you’re in for.

Good luck.

Disclaimer: This information has been provided for educational purposes only and should not be considered financial advice. Any opinions expressed are my own and may not be appropriate in all cases. All efforts have been made to provide accurate information; however, mistakes happen, and laws change; information may not be accurate at the time you read this. Please seek out a licensed professional for current advice specific to your situation.